one to one
a correspondence Column
Sir,
Your article on "Sphere Packing", by Davicl Killen, in MANIFOLD~8 prompts
me to write as to the possibility of an article (riot by me! I have no
idea how to approach this) dealing with the arrangement of spheres such
that they obey the following rules:
(1) All spheres are distinct.
(2) Each sphere touches at least one other sphere.
(3) The centres of the spheres describe a regular lattice.
(4) There is no space between any two spheres such that, if a sphere can
exist in that space, a sphere does not exist there.
(4a) If such a space described in (4) exists then it is occupied by a
sphere conforming to all the rules laid down.
(5) There is no point common to the interiors of any two spheres.
(6) The spheres are so arranged that they occupy the greatest space possible.
i.e.: minimize the density.
Philip Hart
David Killen sent us the
following corrections to his article:
(i) On page 31, the formula for V2n+1 should be multiplied
by n! (factorial).
(ii) Contrary to page 33, one of the maximal packings for 3- dimensions
is cleverly hidden in the packing described for 4-dimensions.
(iii) Each sphere in the 4-dimensional packing touches 24 other spheres,
not 16.
Sir,
I enjoyed doing the computer crossword but when I looked up the solution
I was disturbed to find that I had apparently got G wrong(MANIFOLD-9).
I made it too-pod but the answer given was totter-pod - a difference of
ooty pohl. However, we are agreed that J is poot oddy-tee ohly-too, with
which my value of G and not yours is consistent; I conclude that some-one
mistook a pohl for a poot.
Dinah Forth
(For an explanation of the Pohlish language see MANIFOLD-6 Ed.)